Question

The linear momentum of a projectile varies with time asp = ao + at + bt2. Which of the following represents force and time
relation graphs?
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Answer 1

The linear momentum of a projectile varies with time as P = a₀ + at + bt².

represent the relation between force and time and also its graph.

solution : we know, rate of change of linear momentum with respect to time is equal to force.

i.e., F = dP/dt

here P = a₀ + at + bt².

differentiating P with respect to time t,

dP/dt = F = d( a₀ + at + bt²)/dt

⇒ F = a + 2bt

here it is clear that F is directly proportional to time. and it is linearly variable with time.

now let's draw the graph of force and time.

if we assume y - axis is force and x - axis is time.

then, graph of force and time will be shown in figure.